Power transformer is one of the key equipment in power systems, and higher requirements on the capacity, efficiency, size, and stability are generated from the utilities. An accurate and efficient design process, especially the thermal design, is crucial to fulfill these requirements. In order to tackle the existing problems in transformer cooling, the transformer analysis and design methods are investigated along with the application of a novel coolant, namely, nanofluid. An adaptive degrees-of-freedom (DoFs) finite element method (FEM) solver is developed for the 3-dimensonal (3D) coupled magneto-thermal field analysis, which is based on the independent solvers for the magnetic field and thermal field. In the adaptive DoFs FEM, the system size reduction is realized by eliminating the redundant DoFs from the unknown list rather than removing the corresponding nodes, which is adopted in conventional adaptive FEMs. Hence the rearrangement of mesh data and the storage space for the former mesh are avoided. The slave-master technique is employed in the elimination process in combination with the constraint proposed for 3D field. One set of FEM mesh is used in the coupled magneto-thermal analysis to build the finite element (FE) spaces for these two fields, and the DoFs in each field are adjusted separately according to the field's requirement in discretization. Hence, the different discretization requirements of these two fields are met with one set mesh, and the mapping algorithms for different meshes are no longer required. Several numerical examples are solved to showcase the effectiveness of this method in terms of efficiency and accuracy.Excessive temperature rises of hot-spots, which are commonly located in the windings, accelerate the aging of insulating materials and reduce the transformer service life. In addition, the electrification of oil is exacerbated by the increased flow velocity. The novel coolant, i.e. nanofluid, has the potential to reduce the hot-spot temperature rise by improving the thermal conductivity. In order to apply the nanofluid in transformer cooling, the convective heat transfer of oil/SiC nanofluid in disc-type transformer windings is numerically investigated. The computational fluid dynamics (CFD) model and numerical method used in the study are validated with the existing results of oil cooled transformer windings. One pass of the winding is modelled numerically, in which two different inlet position are concerned. It is the first time to use the multi-phase mixture model to analyze such a nanofluid flow. In addition, the single-phase model is also employed for mutual authentication and comparison. Although the effects that the oil/SiC nanofluid of 1% concentration has on the flows in passes of different inlet positions vary, comprehensive temperature drop over these two types of passes is observed after adding the nanoparticles. For the pass with inlet in the internal vertical duct, the ameliorative mass flow rate distribution further improves the heat transfer performance. In addition, the relation between the volume fraction of nanoparticles and the effect on the thermal and fluidic field is positive. To further investigate the nanofluid flow in disc-type transformer windings, a numerical mode is built for the entire winding with four passes. The results show that there is an overall reduction on the disc average temperature after adding nanoparticles, and the temperature distribution along the passes is maintained. It can be concluded that the heat transfer improvement after using nanofluid is mainly produced by the enhanced thermal conductivity, and the mass flow rate distribution changes produce the inhomogeneous temperature reduction of discs. In addition, the lower coolant temperature enhances the effect of nanofluid in the fourth pass. Since the numerical analysis process is exceedingly time-consuming, a response surface optimization method is proposed to improve the efficiency of oil-immersed transformers cooling system design. Based on the accurate CFD modeling and the central composite design method, surrogate models, which are used to replace the initial CFD model in the optimization, are produced by these two adopted response surface methods, namely, the Kriging method and the second order polynomial method. Refinement points are gradually added into the set of design points until the derived surrogate models meet the predefined criterion. The surrogate model obtained with the Kriging method, which is validated to be more accurate, is adopted in the response surface optimization process, and the direct optimization method combined with the CFD model is also adopted for comparison. An oil-immersed transformer optimization problem is employed to showcase the effectiveness of this proposed optimization method, in which roughly 40% of the computational resources used in the direct optimization method are saved by the proposed method.

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